In competitive inhibition, the molecule acts on the same active site as the normal enzyme substrate. The substrate molecules cannot enter the active site while the inhibitor is there, and inhibitors cannot enter the site when the substrate is there. Characteristic for this mode of inhibition is that increasing the concentration of substrate reduces the effect of the inhibitor, and vice-versa.
In noncompetitive inhibition, the inhibitor works by occupying some other site on the enzyme. Because of this, the substrate and inhibitor do not compete for access to the same site. Rather, the inhibitor alters the shape of the enzyne in such a way that prevents the substrate from binding to the enzyme. In this mode of inhibition, the activity of the enzyme is completely blocked by the inhibitor and increasing the concentration of substrate does not restore enzyme activity.
The kinetics of these activities is described by the Michaelis-Menten equations.